It is correct because:
(-2)⁴ = (-2)*(-2)*(-2)*(-2) = 4*4 = 16
Yes, it can be use as a base to rewrite 64 but not for 32
Because:
(-2)⁶ = (-2)*(-2)* (-2)*(-2) * (-2)*(-2) = 4*4*4 = 16*4 = 64
(-2)⁵ = (-2)*(-2)*(-2)* (-2)*(-2) =4*4*(-2) = 16*(-2) = -32
-32 ≠ 32